Group.Field

Documentation

class (Arbitrary g, Eq g, Generic g, Monoid g, Pretty g, Random g, Show g) => Group g where

Groups.

Minimal complete definition

add, dbl, def, gen, id, inv, order

Methods

add :: g -> g -> g

Element addition.

dbl :: g -> g

Element doubling.

def :: g -> Bool

Check well-defined.

gen :: g

Group generator.

id :: g

Identity element.

inv :: g -> g

Element inversion.

mul' :: g -> Integer -> g

Element multiplication.

order :: g -> Integer

Curve order.

rnd :: MonadRandom m => m g

Random element.

Instances

FGroup k => Group (Element k)

Defined in Group.Field

Methods

add :: Element k -> Element k -> Element k

dbl :: Element k -> Element k

def :: Element k -> Bool

gen :: Element k

id :: Element k

inv :: Element k -> Element k

mul' :: Element k -> Integer -> Element k

order :: Element k -> Integer

rnd :: MonadRandom m => m (Element k)

WPCurve e q r => Group (WPPoint e q r)

Defined in Curve.Weierstrass

Methods

add :: WPPoint e q r -> WPPoint e q r -> WPPoint e q r

dbl :: WPPoint e q r -> WPPoint e q r

def :: WPPoint e q r -> Bool

gen :: WPPoint e q r

id :: WPPoint e q r

inv :: WPPoint e q r -> WPPoint e q r

mul' :: WPPoint e q r -> Integer -> WPPoint e q r

order :: WPPoint e q r -> Integer

rnd :: MonadRandom m => m (WPPoint e q r)

WJCurve e q r => Group (WJPoint e q r)

Defined in Curve.Weierstrass

Methods

add :: WJPoint e q r -> WJPoint e q r -> WJPoint e q r

dbl :: WJPoint e q r -> WJPoint e q r

def :: WJPoint e q r -> Bool

gen :: WJPoint e q r

id :: WJPoint e q r

inv :: WJPoint e q r -> WJPoint e q r

mul' :: WJPoint e q r -> Integer -> WJPoint e q r

order :: WJPoint e q r -> Integer

rnd :: MonadRandom m => m (WJPoint e q r)

WACurve e q r => Group (WAPoint e q r)

Defined in Curve.Weierstrass

Methods

add :: WAPoint e q r -> WAPoint e q r -> WAPoint e q r

dbl :: WAPoint e q r -> WAPoint e q r

def :: WAPoint e q r -> Bool

gen :: WAPoint e q r

id :: WAPoint e q r

inv :: WAPoint e q r -> WAPoint e q r

mul' :: WAPoint e q r -> Integer -> WAPoint e q r

order :: WAPoint e q r -> Integer

rnd :: MonadRandom m => m (WAPoint e q r)

MACurve e q r => Group (MAPoint e q r)

Defined in Curve.Montgomery

Methods

add :: MAPoint e q r -> MAPoint e q r -> MAPoint e q r

dbl :: MAPoint e q r -> MAPoint e q r

def :: MAPoint e q r -> Bool

gen :: MAPoint e q r

id :: MAPoint e q r

inv :: MAPoint e q r -> MAPoint e q r

mul' :: MAPoint e q r -> Integer -> MAPoint e q r

order :: MAPoint e q r -> Integer

rnd :: MonadRandom m => m (MAPoint e q r)

EPCurve e q r => Group (EPPoint e q r)

Defined in Curve.Edwards

Methods

add :: EPPoint e q r -> EPPoint e q r -> EPPoint e q r

dbl :: EPPoint e q r -> EPPoint e q r

def :: EPPoint e q r -> Bool

gen :: EPPoint e q r

id :: EPPoint e q r

inv :: EPPoint e q r -> EPPoint e q r

mul' :: EPPoint e q r -> Integer -> EPPoint e q r

order :: EPPoint e q r -> Integer

rnd :: MonadRandom m => m (EPPoint e q r)

EACurve e q r => Group (EAPoint e q r)

Defined in Curve.Edwards

Methods

add :: EAPoint e q r -> EAPoint e q r -> EAPoint e q r

dbl :: EAPoint e q r -> EAPoint e q r

def :: EAPoint e q r -> Bool

gen :: EAPoint e q r

id :: EAPoint e q r

inv :: EAPoint e q r -> EAPoint e q r

mul' :: EAPoint e q r -> Integer -> EAPoint e q r

order :: EAPoint e q r -> Integer

rnd :: MonadRandom m => m (EAPoint e q r)

BPCurve e q r => Group (BPPoint e q r)

Defined in Curve.Binary

Methods

add :: BPPoint e q r -> BPPoint e q r -> BPPoint e q r

dbl :: BPPoint e q r -> BPPoint e q r

def :: BPPoint e q r -> Bool

gen :: BPPoint e q r

id :: BPPoint e q r

inv :: BPPoint e q r -> BPPoint e q r

mul' :: BPPoint e q r -> Integer -> BPPoint e q r

order :: BPPoint e q r -> Integer

rnd :: MonadRandom m => m (BPPoint e q r)

BACurve e q r => Group (BAPoint e q r)

Defined in Curve.Binary

Methods

add :: BAPoint e q r -> BAPoint e q r -> BAPoint e q r

dbl :: BAPoint e q r -> BAPoint e q r

def :: BAPoint e q r -> Bool

gen :: BAPoint e q r

id :: BAPoint e q r

inv :: BAPoint e q r -> BAPoint e q r

mul' :: BAPoint e q r -> Integer -> BAPoint e q r

order :: BAPoint e q r -> Integer

rnd :: MonadRandom m => m (BAPoint e q r)

newtype Element k

Field elements.

Constructors

F k

Instances

Functor Element

Defined in Group.Field

Methods

fmap :: (a -> b) -> Element a -> Element b

(<$) :: a -> Element b -> Element a

Eq k => Eq (Element k)

Defined in Group.Field

Methods

(==) :: Element k -> Element k -> Bool

(/=) :: Element k -> Element k -> Bool

Read k => Read (Element k)

Defined in Group.Field

Methods

readsPrec :: Int -> ReadS (Element k)

readList :: ReadS [Element k]

readPrec :: ReadPrec (Element k)

readListPrec :: ReadPrec [Element k]

Show k => Show (Element k)

Defined in Group.Field

Methods

showsPrec :: Int -> Element k -> ShowS

show :: Element k -> String

showList :: [Element k] -> ShowS

Generic (Element k)

Defined in Group.Field

Associated Types

type Rep (Element k) :: Type -> Type

Methods

from :: Element k -> Rep (Element k) x

to :: Rep (Element k) x -> Element k

FGroup k => Semigroup (Element k)

Defined in Group.Field

Methods

(<>) :: Element k -> Element k -> Element k

sconcat :: NonEmpty (Element k) -> Element k

stimes :: Integral b => b -> Element k -> Element k

FGroup k => Monoid (Element k)

Defined in Group.Field

Methods

mempty :: Element k

mappend :: Element k -> Element k -> Element k

mconcat :: [Element k] -> Element k

FGroup k => Random (Element k)

Defined in Group.Field

Methods

randomR :: RandomGen g => (Element k, Element k) -> g -> (Element k, g)

random :: RandomGen g => g -> (Element k, g)

randomRs :: RandomGen g => (Element k, Element k) -> g -> [Element k]

randoms :: RandomGen g => g -> [Element k]

randomRIO :: (Element k, Element k) -> IO (Element k)

randomIO :: IO (Element k)

FGroup k => Arbitrary (Element k)

Defined in Group.Field

Methods

arbitrary :: Gen (Element k)

shrink :: Element k -> [Element k]

NFData k => NFData (Element k)

Defined in Group.Field

Methods

rnf :: Element k -> ()

FGroup k => Pretty (Element k)

Defined in Group.Field

Methods

pretty :: Element k -> Doc

prettyList :: [Element k] -> Doc

FGroup k => Group (Element k)

Defined in Group.Field

Methods

add :: Element k -> Element k -> Element k

dbl :: Element k -> Element k

def :: Element k -> Bool

gen :: Element k

id :: Element k

inv :: Element k -> Element k

mul' :: Element k -> Integer -> Element k

order :: Element k -> Integer

rnd :: MonadRandom m => m (Element k)

type Rep (Element k)

Defined in Group.Field

type Rep (Element k) = D1 (MetaData "Element" "Group.Field" "elliptic-curve-0.2.1-JwwOFk1u1pTLWrP9gZwWus" True) (C1 (MetaCons "F" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 k)))

class GaloisField k => FGroup k where

Field groups.

Methods

g_

Arguments

:: Element k

Group generator.

q_

Arguments

:: Element k

-> Integer

Group characteristic.

r_

Arguments

:: Element k

-> Integer

Group order.

x_

Arguments

:: k

Group element.

Instances

FGroup Fq12

BN254TF group is a field group.

Defined in Group.Field.BN254TF

Methods

g_ :: Element Fq12

q_ :: Element Fq12 -> Integer

r_ :: Element Fq12 -> Integer

x_ :: Fq12